Book 2006

Algebra

Fields and Galois Theory

Authors:

ISBN: 978-0-387-28930-4 (Print) 978-0-387-31608-6 (Online)

Table of contents (19 chapters)

  1. Front Matter

    Pages i-vii

  2. Chapter

    Pages 1-13

    Constructibility with Ruler and Compass

  3. Chapter

    Pages 15-20

    Algebraic Extensions

  4. Chapter

    Pages 21-32

    Simple Extensions

  5. Chapter

    Pages 33-43

    Fundamentals of Divisibility

  6. Chapter

    Pages 45-53

    Prime Factorization in Polynomial Rings. Gauss’s Theorem

  7. Chapter

    Pages 55-64

    Polynomial Splitting Fields

  8. Chapter

    Pages 65-73

    Separable Extensions

  9. Chapter

    Pages 75-82

    Galois Extensions

  10. Chapter

    Pages 83-92

    Finite Fields, Cyclic Groups and Roots of Unity

  11. Chapter

    Pages 93-101

    Group Actions

  12. Chapter

    Pages 103-113

    Applications of Galois Theory to Cyclotomic Fields

  13. Chapter

    Pages 115-131

    Further Steps into Galois Theory

  14. Chapter

    Pages 133-141

    Norm and Trace

  15. Chapter

    Pages 143-164

    Binomial Equations

  16. Chapter

    Pages 165-190

    Solvability of Equations

  17. Chapter

    Pages 191-202

    Integral Ring Extensions with Applications to Galois Theory

  18. Chapter

    Pages 203-208

    The Transcendence of π

  19. Chapter

    Pages 209-216

    Fundamentals of Transcendental Field Extensions

  20. Chapter

    Pages 217-230

    Hilbert’s Nullstellensatz

  21. Back Matter

    Pages 231-293